A honeycomb structure in which predetermined cells are plugged by a plugging material has heretofore been used as a filter (e.g., a diesel particulate filter: DPF) for trapping/removing particulate matters included in dust-containing fluids such as an exhaust gas exhausted from a diesel engine (see Japanese Patent Application Laid-Open No. JP-A-7-332064, for example). Moreover, in recent years, porosities of partition walls of the honeycomb structure have been increased in order to reduce a pressure loss in treating the exhaust gas in the honeycomb structure and to treat the exhaust gas more efficiently (see Japanese Patent Application Laid-Open No. JP-A-2002-219319, for example). However, to proceed with the increases of the porosities of the partition walls of the honeycomb structure, as shown in FIG. 2, there has been a problem that cracks 5 are easily generated in cell walls 2 of an end portion (end face) of a honeycomb structure 1. A honeycomb structure 1 shown in FIG. 2 has a plurality of cells 4, each cell 4 being surrounded by cell walls 2 and functioning as a fluid passage. Predetermined cells 4 are plugged by a plugging material at one end face to form plug portion 3. Remaining cells 4 are plugged by the plugging material at the other end face (not shown).